BACKGROUND: Large language models (LLMs) hold potential for mental health applications. However, their opaque alignment processes may embed biases that shape problematic perspectives. Evaluating the values embedded within LLMs that guide their decision-making have ethical importance. Schwartz's theory of basic values (STBV) provides a framework for quantifying cultural value orientations and has shown utility for examining values in mental health contexts, including cultural, diagnostic, and therapist-client dynamics. OBJECTIVE: This study aimed to (1) evaluate whether the STBV can measure value-like constructs within leading LLMs and (2) determine whether LLMs exhibit distinct value-like patterns from humans and each other. METHODS: In total, 4 LLMs (Bard, Claude 2, Generative Pretrained Transformer [GPT]-3.5, GPT-4) were anthropomorphized and instructed to complete the Portrait Values Questionnaire-Revised (PVQ-RR) to assess value-like constructs. Their responses over 10 trials were analyzed for reliability and validity. To benchmark the LLMs' value profiles, their results were compared to published data from a diverse sample of 53,472 individuals across 49 nations who had completed the PVQ-RR. This allowed us to assess whether the LLMs diverged from established human value patterns across cultural groups. Value profiles were also compared between models via statistical tests. RESULTS: The PVQ-RR showed good reliability and validity for quantifying value-like infrastructure within the LLMs. However, substantial divergence emerged between the LLMs' value profiles and population data. The models lacked consensus and exhibited distinct motivational biases, reflecting opaque alignment processes. For example, all models prioritized universalism and self-direction, while de-emphasizing achievement, power, and security relative to humans. Successful discriminant analysis differentiated the 4 LLMs' distinct value profiles. Further examination found the biased value profiles strongly predicted the LLMs' responses when presented with mental health dilemmas requiring choosing between opposing values. This provided further validation for the models embedding distinct motivational value-like constructs that shape their decision-making. CONCLUSIONS: This study leveraged the STBV to map the motivational value-like infrastructure underpinning leading LLMs. Although the study demonstrated the STBV can effectively characterize value-like infrastructure within LLMs, substantial divergence from human values raises ethical concerns about aligning these models with mental health applications. The biases toward certain cultural value sets pose risks if integrated without proper safeguards. For example, prioritizing universalism could promote unconditional acceptance even when clinically unwise. Furthermore, the differences between the LLMs underscore the need to standardize alignment processes to capture true cultural diversity. Thus, any responsible integration of LLMs into mental health care must account for their embedded biases and motivation mismatches to ensure equitable delivery across diverse populations. Achieving this will require transparency and refinement of alignment techniques to instill comprehensive human values.